The topology relation of low voltage distribution network is the basis of power network state estimation.Article in view of the low voltage distribution network topology identification problems, this paper analyzes the change relation through the voltage similar and the feasibility of the phase identification, based on the application of Hausdorff distance algorithm, build the similarity assessment based on node voltage and phase change relation recognition process, design the basic criterion of recognition, and including the construction of sliding window and select the effective voltage data collection optimization method;Finally, the effectiveness of the proposed method is verified by a practical case.